He joins Jack Nicklaus, Tom Watson, Tom Kite and Tiger Woods as US Open champions at the famous California links and said afterwards: "I can't believe I'm standing here with this (trophy).
"I've dreamed of this all my life, two putts to win the US Open, and I couldn't believe I had a 20-footer to do that. This thing feels amazing."
Trailing by three at the start of the day, McDowell watched playing partner Dustin Johnson throw away his three-shot lead with a seven at the par-four second and add a double-bogey at the third.
Ernie Els briefly shared the lead at three under through six but neither he nor the likes of Tiger Woods and Phil Mickelson could mount a serious challenge.
It was left to Havret to carry the fight but when he missed a birdie putt at the last, McDowell needed only a par and immediately told caddie Ken Comboy: "I like the lay-up".
He elaborated afterwards: "It's very tough to make birdies - you go chasing and you'll make bogeys.
"After the way Dustin played yesterday, I thought if the same guy turned up today he'd be really tough to beat but I just tried to concentrate on my own game.
"I was debating whether to have a go (at the 18th green) in two but when I saw Greg miss his putt, I completely bailed out of that idea.
"I got the nine iron out, left myself my nice number, 100 yards, and got it on the green.
"Greg played fantastic golf the last couple of days. I'm just so thrilled to get over the line.
"I can't believe how difficult this course was. I bogeyed 10 and had a little peek at the leaderboard - no-one was going crazy and I couldn't believe it.
"There's bogeys out here, it doesn't matter how well you play. I think everyone really enjoyed the test this week, it was fair - good golf got rewarded and bad golf got punished pretty badly."
Havret admitted to mixed feelings, telling Sky Sports 1: "I'm caught in between the best surprise of my life and the biggest disappointment too. I'm second, which is probably the worst place, but it's such a dream to play good golf here, four rounds beautifully.
"I came up one short, it's a shame those two putts at 18 and 17 were not good enough to put my name at the top of the leaderboard.
"I'm happy it went to the 72nd hole, I didn't make any big mistakes."
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